limit, we show that these apparent anomalies originate from lattice effects and an underlying integrable structure. In particular, we map the post-quench dynamics onto an integrable Neumann system and we derive a new action-angle description valid in the thermodynamic limit. This framework explains both the convergence of long-time averages to the generalized Gibbs ensemble and the emergence of persistent oscillations associated with an isolated mode at the upper edge of the phonon spectrum. We further show that the expected thermal universality class is recovered in the appropriate scaling regime, while the oscillations disappear in the quantum field theory limit.

DOI: 10.1103/nh76-cb9q

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O(n)

model in the large-

n

g

) and longitudinal (

h

) magnetic fields. This model exhibits a continuous quantum transition (CQT) at

g=g_c

and

h=0

, and first-order quantum transitions (FOQTs) driven by

h

along the line

h=0

(

g<g_c

). In the integrable limit

h=0

, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value

h_i < 0

to a positive value

h_f>0

. We focus on values of

h_f

such that the spectrum of the post-QQ Hamiltonian

H(g,h_f)

lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of

g

, finding qualitatively distinct behaviors for

g > g_c

(where the chain is in the disordered phase), for

g = g_c

(QQ across the CQT), and for

g<g_c

(QQ across the FOQT line).

\mathit{XY}

quantum spin chain in a transverse field, we characterize the nonequilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasiparticle excitation that ensure that Kibble-Zurek scaling persists. The emergence of effective thermal equilibrium behavior following a sudden quench toward criticality is also investigated, with focus on the long-time expectation value of the quasiparticle number operator. Despite the integrability of the

\mathit{XY}

model, this observable is found to behave thermally in quenches to a regular quantum critical point, provided that the system is initially prepared at sufficiently high temperature. However, a similar thermalization behavior fails to occur in quenches toward a multicritical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.

We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter

g

driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of

g

around the critical value

{g}_{c}

, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of

g

. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest-neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular, the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.